Sketch the region bounded by the graphs of the algebraic functions and find the area of the region: f(x) = 1/2x3 +2; y= x+1; x=0; x=2
Answers
The area of the region bounded by curve f(x) and y = x+1 and the vertical lines x=0 and x=2 is 2 square units.
To sketch the region, we first plot the curves: f(x) = 1/2x^3 +2 is a cubic function that passes through the point (0,2) and (2,6). y = x+1 is a straight line that passes through the points (0,1) and (2,3). The region is bounded by the x-axis, the vertical lines x=0 and x=2, and the curves f(x) and y = x+1.
To find the area of the region, we can integrate the difference between the curves with respect to x, from x=0 to x=2:
Area = ∫[0,2] (x+1 - 1/2x^3 -2) dx
Simplifying this expression, we get:
Area = ∫[0,2] (-1/2)x^3 + x dx
= [-1/8 x^4 + 1/2 x^2] from 0 to 2
= 2
Therefore, the area of the region is 2 square units.
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Related Questions
You have been given the task of organizing a poll regarding an upcoming election. The object is to estimate the proportion of the country that will vote to keep the current government in power. You have been told to collect a sample and find a 95% confidence interval for the proportion. This interval is allowed to have a margin of error of 3%. A preliminary investigation suggests that the proportion of people that will vote to keep the current government is 0.74. a) Calculate the minimum sample size that is required in this survey. Give your answer as a whole number. Someone working on your team reports that the information suggesting that the proportion of people that will vote to keep the current government is equal to 0.74 is out of date. In fact, some recent events in politics mean that there is no safe guess at what the proportion might be. b) Based on this new information, calculate the minimum sample size that is required in this survey. Give your answer as a whole number.
Answers
The confidence interval for the task of organizing the poll for the upcoming elections be,
(222.117 , 257.883)
Given, You have been given the task of organizing a poll regarding an upcoming election.
The object is to estimate the proportion of the country that will vote to keep the current government in power.
You have been told to collect a sample and find a 95% confidence interval for the proportion.
This interval is allowed to have a margin of error of 3%. A preliminary investigation suggests that the proportion of people that will vote to keep the current government is 0.74.
We have to find the confidence interval,
Subtract 1 from your sample size. 10 – 1 = 9.
Subtract the confidence level from 1, then divide by two.
(1 – .95) / 2 = .025
For 9 degrees of freedom df and α = 0.025, margin of error is 2.262.
Divide your sample standard deviation by the square root of your sample size.
25 / √(10) = 7.90569415
Now, Multiply 2.262 × 7.90569415 = 17.8826802
For the lower end of the range
240 – 17.8826802 = 222.117
For the upper end of the range
240 + 17.8826802 = 257.883
Hence, the confidence interval be (222.117 , 257.883)
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The middle 5 in 0.555is 10 times the value of the 5 to its
Answers
Numbers increase in value as you go right to left
The population of a town has beca decreasing since 1991 . The poptilation of the town was 26,700 people in the year 1995 . In the year 2003 , the population of the town had decreased to 20,300 people.
1. Find the linear function P=m t+b that models the town's population P as a function of the number of years, t, since 1991.
i. Find a reasonable domain for the function P.
Domain:
ii. Find a reasonable range for the function P
Range:
iv. Interpret the slope of the function P
Answers
1. The linear function that models the town's population is given as follows:
P(t) = -640t + 26,700.
i. The domain for the function is of: t ≥ 0.
ii. The range for the function is of: 0 ≤ P(t) ≤ 26700.
iv. The slope of -640 means that the population decayed by an average of 640 habitants each year.
What is the linear function?The function is defined as follows:
P(t) = mt + b.
In which the parameters are listed as follows:
m is the slope, representing the rate of change.b is the intercept, representing the initial population.In 10 years, the population decreased from 26,700 to 20,300, hence the slope is of:
m = (20,300 - 26,700)/10 = -640.
Considering the population in 1995, the intercept is given as follows:
b = 26,700.
Hence the equation is given by:
P(t) = -640t + 26,700.
The domain and range of the function are given as follows:
i. The domain for the function is of: t ≥ 0, as it is the number of years after 1995.ii. The range for the function is of: 0 ≤ P(t) ≤ 26700, as it is the values assumed by the population.More can be learned about linear functions at https://brainly.com/question/24808124
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Answer:b-of the AAS congruence theorem.
Step-by-step explanation: I guessed and got it right
mikes's fittness center charges $30 per month for a membership. all day fitness club charges $22 per month plus an $80 initiation fee for a membership. after how many months will the total amount paid to the two fitness clubs be the same
Answers
Answer: 7 months
Step-by-step explanation: by 7 months you would have paid both memberships $300
i would do 100 points but i cant i only have 33 please give me the right answer or i will report
Answers
Answer:
heightwidthid-kwidthbasesquareStep-by-step explanation:
749/d * d/749 = 1
d=?
Answers
Answer:
D=1
Step-by-step explanation:
1. Combine multiplied terms into a single fraction
2. Cancel terms that are in both numerator and denominator
3. Divide by 1
Answer:
I honestly don't know but I think its all real numbers but not zero
Step-by-step explanation:
1. ¿Cuántas millas por minuto son 55 millas por hora?
Answers
Answer:
0.91
Step-by-step explanation:
After a rotation, A(–3, 4) maps to A'(4, 3), B(4, –5) maps to B'(–5, –4), and C(1, 6) maps to C'(6, –1). Which rule describes the rotation? R0, 90° R0, 180° R0, 270° R0, 360°
Answers
Answer: R0, 270°
Step-by-step explanation: i have the answers to all the quetions
on the quiz/ assignments you doing. i can send u the l i n k if u want.
Answer:
R0, 270 is the correct Answer!
Step-by-step explanation:
Hope this helps =)
A function and its inverse are shown on the same graph.
f(x)
x
6.
Which statement describes the relationship between the
function and its inverse?
O The slope of f¹(x) is the same as the slope of f(x).
The slope of f¹(x) is the opposite as the slope of f(x).
O The x-intercept of f¹(x) is the same as the y-intercep
of f(x).
The x-intercept of f¹(x) is the opposite as the y-
intercept of f(x).
Answers
Answer:
(c) The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).
Step-by-step explanation:
You want to know the relationship between the graphs of function f(x) and its inverse f⁻¹(x).
Inverse functionThe inverse of a function maps every y-value of the original function to its corresponding x-value. That is if you have ...
f(a) = b
then the graph of f(x) contains the ordered pair (a, b).
The inverse function will have the ordered pair (b, a). That is,
f⁻¹(b) = a
ApplicationIf an ordered pair (x-intercept) of the inverse function is ...
(P, 0)
Then there will be an ordered pair (0, P) on the graph of the original function. That point is the y-intercept, and its y-coordinate is the same as the x-coordinate of the x-intercept of the inverse function.
The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).
__
Additional comment
The graphs of the two functions are mirror images of each other across the line y=x.
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Ximena pays a flat cost of $44.50 per month and $4 per gigabyte. She wants to keep her bill at $50.10 per month. How many gigabytes of data can she use while staying within her budget?
Answers
Answer:
Ximena can use 1 gigabytes of data
Step-by-step explanation:
The first thing you want to do is subtract
51.10 - 44.50 = 5.6
5.6 is the amount of money she will have to spend on data
With each gigabyte costing 4 dollars and only 5 dollars to spend
she can only use one gigabyte
Which of the following is not a Pythagorean triple?
A. (6, 8, 10)
B. (9, 12, 15)
C. (7, 24, 25)
D. (4, 5, 6)
Answers
Answer:
D. 4, 5, 6, then
H² = P² + B²
6² = 5² + 4²
36 = 25 + 16
36 ≠ 41
This is not Pythagorean triple.
Write an equation in slope-intercept form (-5,-7);y=-2x+4
Answers
Answer:
Step-by-step explanation:
First, let us substitute x and y values: -7 = -2(-5) + 4
Next, let us simplify using the substitution property of equality: 14 = -7 (SEE BELOW MORE INFO).
Now, this does not make sense yet because 14 cannot possibly equal -7. Therefore, we must add a b value, therefore leading us to the equation:
14 + b = -7
by simplifying, we can conclude that b = -21
Finally, we can plug in the b-value into our original equation:
y = -2x + 4 - 21
After simplifying, we get y = -2x - 17. When this is graphed, we can see that -2x - 17 intersects (-5, -7).
Choose the word or phrase that correctly completes the sentence.
Andrew wrapped his
sisters
sisteres'
sisters'
sister's
I don't know this yet.
present.
Answers
Answer:
answer is sister's.
Step-by-step explanation:
sisters mean more than one sister.
sisterses isn't a word.
sisters' also isn't a word.
sister's is a word and it means that she has possession of something or that she owns something.
Please help I’m stuck
Answers
Answer:
96
Step-by-step explanation:
Its a pattern :) BTW can you help with mine please
Omar jarred 6 liters of jam after 3 days. How many days does Omar need to spend making jam if he wants to jar 10 liters of jam in all? Assume the relationship is directly proportional.
Answers
To solve the exercise you can use a rule of three, like this
\(\begin{gathered} 6\text{ liters}\rightarrow3\text{ days} \\ 10\text{ liters}\rightarrow x\text{ days} \end{gathered}\)\(\begin{gathered} x=\frac{10\text{ liters }\cdot3\text{ days}}{6\text{ liters}} \\ x=\frac{10\cdot3\text{ days}}{6} \\ x=\frac{10\cdot3}{6}\text{days} \\ x=\frac{30}{6}\text{days} \\ x=5\text{ days} \end{gathered}\)Therefore,
BRAINLLY!!! PLEASE HELP I'll GIVE BRAINLY!!!!
Answers
Answer: 495
Step-by-step explanation:
Since the foil covers the object and does not fill it, this problem is a matter of surface area rather than volume. Surface area is finding the area of all the faces, and adding them up.
Since we know the two triangular ends are not covered, this actually makes the problem easier.
Going with our definition of surface area above, we do:
(16.5 * 13) + (16.5 * 12) + (16.5 * 5) = 495
Our answer is 495
Answer:
C: 495ft²
Step-by-step explanation:
You need to calculate and add the surface area of the three rectangular faces of this prism. The two triangular ends are not covered in the foil as stated in the question. You find this like any other rectangle by multiplying the length by the width. (a = lw)
Let's start with the bottom rectangle, it has dimensions of 5x 16.5ft
5 * 16.5 = 82.5
Now the rectangle on the right side.
13 * 16.5 = 214.5
Now the left or back side rectangle.
12 * 16.5 = 198
Now add these values together
82.5 + 214.5 + 198 = 495ft²
Triangles Q R S and X Y Z are shown. Angles Q S R and X Z Y are right angles. Angles Q R S and X Y Z are congruent. The length of Y Z is 9, the length of X Z is 12, and the length of hypotenuse X Y is 15.
Given △QRS ~ △XYZ, what is the value of tan(Q)?
Three-fifths
Three-fourths
Four-fifths
Answers
Answer:three-fourths
Step-by-step explanation:
because my dad said it was right
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
Answers
b=48(slope-rate of change)
y=44x+48
proportional graph
positive slope
Verify that segments with lengths of 21 inches, 72 inches, and 75 inches form a triangle. If so, determine whether they form a right triangle.
A. triangle, right triangle
B. triangle, isosceles triangle
C. triangle, obtuse triangle
D. triangle, acute triangle
Answers
Answer:
it would be C
Step-by-step explanation:
Find an equation in slope-intercept form for the line containing the following points.
(1,−3) and (3,−5)
Answers
Answer:
y=-x-2
Step-by-step explanation:
slope-intercept form is y = mx+b
slope is change in y over change in x, which is -5-(-3)/(3-1) = -1
y = -x+b
plugging in a point, like (1,-3), we have -3 = -1+b. b = -3+1 = -2
y = -x-2
Slope
m=(-5+3)/3-1m=-2/2m=-1Equation in point slope form
y+3=-1(x-1)y+3=-x+1y=-x+1-3y=-x-2use the drop downs to identify the domain and range of the following relation.
{(-4, -7), (0, 6), (5, -3), (5, 2)}
Answers
Answer:Domain is x and range is y.For ex:-4 is domain and -7 is range.
Step-by-step explanatioFeel pleasure to help u:
Domain ( -4, 5) Range ( -7, 6)
The Domain includes the numbers between the least and the greatest x-values.
The range includes the numbers between the lowest and the highest y-values.
How do I Solve for h A=9h h=
Answers
Answer:
h=A/9
Step-by-step explanation:
41 is what percent of 120
Answers
Answer: Approximately 34.17%.
Step-by-step explanation: Let's divide 41 by 120. Doing so, we get 0.3466666 looping forever. We can simplify that to .3417, and then turn that into a percentage giving us 34.17%
I need Help please!!!
Answers
Step-by-step explanation:
it seems you solved the tricky part yourself already.
just to be sure, let's do the first derivative here again.
the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...
f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =
= 3t⁴ + 18t³ + 24t² + 18t + 21
f'(t) = 12t³ + 54t² + 48t + 18
and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).
we simply put the input number (2) at every place of the input variable (t).
so,
f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =
= 426
if x=3, what is Y?
x= -3,0,3,6
y= -5,-4,-3,-2
Answers
Answer:
If x = 3, then y = -2 since the corresponding value of y for x=3 is -2 in the given table.
Step-by-step explanation:
What is the diameter of a circle with the equation x2 + y2 - 8x + 2y - 8 = 0?
5 units
6 units
9 units
10 units
Answers
Answer:
Diameter is 10 units
Step-by-step explanation:
Convert standard form to general form by completing the square:
\(x^2+y^2-8x+2y-8=0\)
\(x^2-8x+y^2+2y-8=0\)
\(x^2-8x+y^2+2y=8\)
\(x^2-8x+16+y^2+2y+1=8+16+1\)
\((x-4)^2+(y+1)^2=25\)
\((x-4)^2+(y+1)^2=5^2\)
So, since the radius of the circle is 5 units, then the diameter is twice the radius, which is 10 units.
Answer:
50
Step-by-step explanation:
x2 + y2 - 8x + 2y - 8 = 0
first we find the radius with the equation.
write the equation in standard form.
x2 + y2 - 8x + 2y - 8 = 0
(x-4)^2 + (y+1)^2 = 25
(x-h)² + (y-k)² = r²
this means 25 is the radius and the diameter is two times the radius so,
25 x 2 = 50
Find the interquartile range of the data. 19, 11, 15, 10, 20, 15, 28, 22, 17 IQR
Answers
Answer:
Interquartile Range: 8
Step-by-step explanation:
25th Percentile: 13
50th Percentile: 17
75th Percentile: 21
So the answer must be 8
Hope this helps :)
Please help asap!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
−
2
g
+
20
h
+
1
Step-by-step explanation:
Answer:
Its 13
Step-by-step explanation:
The town of Winchester recently built an artificial body of Vater. This reservoir will store drinking water for the
town. Which of the following could cause contamination of the water and lead to human health-related problems
and loss of native species?
development of a water quality plan
B building a fence around the reservoir
C improvements to a water treatment facility
increased use of pesticides (chemicals) by farmers within the local watershed
Answers
Answer:
This reservoir, will store drinking water for the town. Which of the following could cause contamination of the water and lead to human health-related problems and loss of native species? ... Air pollution can affect human health and the health of other living things.
Step-by-step explanation:
13 cm
L
5 cm
Calculate the perimeter
Answers
Answer:
36
Step-by-step explanation:
permeter is solved by doing length+length+width+width so therefore you would do 13+13+5+5 which equals 36 as your answer